Closely related to the card game Mao, despite being different in almost every conceivable way. On the other hand, this being different is true between individual games of Mao, and of Calvinball. So this may be more of a similarity than a difference. Er... let's move on. ;)

There is one critical distinction (which I think I may mention, even under the rule of Mao): There are reasonably standard rules to Mao, and when they change at all, the rules tend to accrete, rather than being continuously reset as in Calvinball.

The other major difference is that it is almost impossible to actually play this game unless one person is all of the players. Calvin could get away with this when playing with Hobbes, but Rosalyn had trouble, as shown above. Of course, with a poor Mao-master, Mao is almost impossible to play too.